However, the major talking point of the game was Mourinho's furious reaction to Chelsea assistant coach Ianni, who appeared to cross the line while celebrating Barkley's equaliser.
Mourinho attempted to confront the Chelsea employee, understood to be the club's second assistant coach Marco Ianni, before tempers calmed and the final seconds were allowed to play out.
Chelsea coach Maurizio Sarri backed Mourinho, saying he had already reprimanded his staff member for his role in the incident.
He said: "Oh come on, I can tell you that 97 minutes of the game was so good that you have to focus on that".
"I'm not annoyed with anything", said Mourinho.
Jose Mourinho's latest return to Stamford Bridge was unlikely to ever pass off quietly, but we did not expect it to end with him leaping off his perch in the visiting technical area to hunt down a Chelsea staff member like he suddenly had an Eva Carneiro flashback. I have made a lot of mistakes in my career.
"A passive and anaemic Manchester United first half, second half it very almost became masterclass but it ended with Mourinho showing absolutely no class, none whatsover", Keys said on beINSports' coverage of the game.
Mourinho, who won three titles with Chelsea, has been touted as the next Premier League managerial sacking after his side's indifferent start to the season.
"I didn't see what happened but I have spoken to Jose Mourinho".
"He was very impolite but Sarri took care of the situation".
"We were the best team on the pitch", Mourinho said.
"At 1-1 we stopped with our football and played other football". "We have more ball so for me it's not bad". "So when he came after the game to make his apologies I accepted his apologies".
"In those hard moments, the moments where he was not selected, not playing regularly, he was saying the same all the time: "I want to play for you and I am going to make it and be the player you want me to be'".
In contrast, Sarri - a relatively late bloomer in elite management after working his way up through the lower tiers of Italian football - is still waiting for his first piece of major silverware, and he believes he has a long way to go to be considered in the same bracket as Mourinho.
"Things were not tense between us to begin with [before the performance at Chelsea]", said Martial.
Martial demonstrated his ice cool finishing with two well taken strikes reminiscent of his first season at the club.
Both players gave it their all in the second half and Martial looked crestfallen when he was substituted with minutes to go.
"It was a big moment for the Chelsea team, fans and staff so they're entitled to over celebrate, you always do with a last minute goal".